State true/ false:

The numbers $14, 58, 1316$ are in descending order.

see full answer

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True

False

answer is B.

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Detailed Solution

Here, we need to find whether the numbers

14, 58, 1316

are in descending order or not.
To compare the rational numbers, their denominators should be the same.
LCM (4, 8, 16) = 16.
So, we convert each rational number to a rational number with denominator 16.

14 = 1 × 4 4 × 4 ⇒ 14 = 416

58 = 5 × 2 8 × 2 ⇒ 58 = 1016

1316 = 13 × 1 16 × 1 ⇒ 1316 = 1316

We observe that

1316 > 1016 > 416,

which when converted in the form of given rational numbers is

1316 > 58 > 14 .

Thus, the given descending order is wrong.
Hence, the statement is false.
Therefore, the correct option is 2.

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